Simulation and Analysis of Anisotropic Coating on

Plane and Curved Surface

Abstract

VirtualLab Fusion provides the capability to

add birefringent coatings, that is, layers of

anisotropic media, to the surfaces of optical

components, in order to exploit the extra

freedom of polarization control and

multiplexing in optical systems. In this

example, we introduce this feature – adding

anisotropic coatings on surfaces – and

investigate the polarization conversion of a

lambda/4 coating on a plane surface and a

curved surface, respectively.

Quarter-Wave Plate Coating on Plane Surface

plane wave- wavelength: 532nm

- polarization state: linearly

polarized along x

- off-axis angle: 0°, 15°, 30°

anisotropic coating- lambda/4 wave plate

- Calcite crystal (uniaxial)

- 𝑛𝑜,𝑒 = (𝐴𝑜,𝑒 +𝐵𝑜,𝑒𝜆

2

𝜆2−𝐶𝑜,𝑒+

𝐷𝑜,𝑒𝜆2

𝜆2−𝐸𝑜,𝑒)0.5

?How does the polarization

state of the input field with

different incident angles

change after passing through

the quarter-wave coating?

detectors- perpendicular to

beam directions

System Building Blocks – Source

A Scanning Source is used to model the input plane

waves. It is a convenient tool for the specification of

several directions simultaneously and for

polarization management.

System Building Blocks – Coating on Surfaces

choose from the predefined

anisotropic media or use a

template medium and

customize the parameters, the

preview of the medium is

shown on the right

With the help of the Waveplate Calculator, the thickness of

the coating layers can be calculated to achieve the desired

retardation between the field components.

Polarization Conversion at a Quarter-Wave Plate

linear

polarization

in

circular

polarization

out

quarter-wave

plate

x

y z 𝐸𝑥

𝐸𝑥 𝐸𝑦

In the idealized situation, when linearly

polarized light impinges on a quarter-wave plate at

45° to the optic axis, the transmitted light is

divided into two equal electric field components.

One of these is retarded by a quarter wavelength

and the overlap of both beams at the exit plane of

the plate generates circularly polarized light. And

vice versa: if the incident light is circularly

polarized, it will be transformed into linearly

polarized light.

Influence of Fresnel Effect Deviation

plane wave- linearly polarized along x

- off-axis angle: 0°, 15°, 30°

𝐸𝑥 𝐸𝑥

𝐸𝑥 after real structured quarter-wave plate with & without AR coating

• However, when a real quarter-wave coating is configured, the two divided

electric field components will face different refraction indices inside the

crystal.

• Hence, the Fresnel effect when leaving the crystal will differ for the two

electromagnetic field components as well, and the polarization state of the

transmitted light will form an ellipse instead of a perfect circle.

• In order to eliminate this influence, an additional anti-reflection coating is

applied together with the crystal coating. Then the perfect circularly

polarized light is observed.

combination of

isotropic AR coating

and anisotropic layer

𝐸𝑥

Quarter-Wave Plate Coating on Plane Surface

𝐸𝑥 after real structured quarter-wave plate with 0°, 15° and 30° of incidence

Another additional effect that might influence the polarization

conversion is the angle of incidence. Due to the projection of the

components of the field on the plane of the plate, the resulting

polarization state will become more elliptical with increasing angle.

𝐸𝑥 𝐸𝑥

plane wave- linearly polarized along x

- off-axis angle: 0°, 15°, 30°

Quarter-Wave Plate Coating on Curved Surface

𝐸𝑥 after real quarter-wave coating on curved surface with 0°, 15° and 30° of incidence

If a quarter-wavelength coating is applied to a curved surface

instead, which curvature allows the light to propagate along the

normal vector of the surface, the effect of different projections of

the field components can be avoided. This results in perfect

circular polarization for all angles of incidence.

𝐸𝑥 𝐸𝑥 𝐸𝑥

plane wave- linearly polarized along x

- off-axis angle: 0°, 15°, 30°

Document Information

10

titleSimulation and Analysis of Anisotropic Coating on Plane and Curved

Surface

document code CRO.0006

version 1.0

edition VirtualLab Fusion Basic

software version 2021.1 (Build 1.180)

category Feature Use Case

further reading

- Optically Anisotropic Media in VirtualLab Fusion

- Conical Refraction in Biaxial Crystals

- Polarization Conversion in Uniaxial Crystals

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